Question

q a car is travelling at 20 m/s along a road .a child runs out into the road 50 m ahead and the car driver steps on the brake pedal.what must the cars deceleration be if the car is to stop just before it reaches the child

Answer 1

Equations of motion: SUVAT  (where s= displacement, u= initial velocity, a= acceleration/deceleration, t= time taken.
v=u + at
v2 = u2 + 2as
s=1/2(u+v)t
s=ut + 1/2at2

In this question we have:

                 initial velocity to be= 20m/s (speed at which car is moving at)
               
                 final velocity to be = 0 m/s  (the car finally stops
                
                 displacement =  50 m (just to the point where the child is)

Therefore we can calculate the deceleration as follows:

V2 = U2 + 2as

0^2= 20^2 + 2(a x 50)

0 =  400 + 2x 50a       0= 400 + 100a

therefore 100a = -400
                   a = -4  (deceleration is negative acceleration)
                     =  -4m/s2

Therefore the car must decelerate at 4m/s2